Towards n-type conductivity in hexagonal boron nitride

Asymmetric transport characteristic in n- and p-type conductivity has long been a fundamental difficulty in wide bandgap semiconductors. Hexagonal boron nitride (h-BN) can achieve p-type conduction, however, the n-type conductivity still remains unavailable. Here, we demonstrate a concept of orbital split induced level engineering through sacrificial impurity coupling and the realization of efficient n-type transport in 2D h-BN monolayer. We find that the O 2pz orbital has both symmetry and energy matching to the Ge 4pz orbital, which promises a strong coupling. The introduction of side-by-side O to Ge donor can effectively push up the donor level by the formation of another sacrificial deep level. We discover that a Ge-O2 trimer brings the extremely shallow donor level and very low ionization energy. By low-pressure chemical vapor deposition method, we obtain the in-situ Ge-O doping in h-BN monolayer and successfully achieve both through-plane (~100 nA) and in-plane (~20 nA) n-type conduction. We fabricate a vertically-stacked n-hBN/p-GaN heterojunction and show distinct rectification characteristics. The sacrificial impurity coupling method provides a highly viable route to overcome the n-type limitation of h-BN and paves the way for the future 2D optoelectronic devices.


Supplementary Note 2: Driving force of O binding to Ge donor
We further performed first-principle calculations on the formation energies of individual GeB impurity, GeB-ON dimer, and GeB-2ON trimer in h-BN monolayer to investigate the driving force of O binding. The formation energies of impurity X is defined as follow: 1 where [ ] is the total energy derived from the system with impurity X doping, [ ] is the total energy of the system before the impurity X doping, ni indicates the number of atoms of type i that have been added (ni >0) or removed (ni <0) from the supercell when the impurity is formed, and the are the chemical potentials of these species. It is interesting to see that the O binding will lower the formation energy of Ge or Ge-O impurities. The decreasing formation energy follows the trend: GeB > GeB-ON > GeB-2ON > GeB-3ON. This implies that the binding and coupling with O could minimized the formation energy of Ge, which is the driving force for the formation preference of Ge-O bonds. More importantly, the formation energies of single O binding to GeB-ON dimer, and O binding to GeB-2ON trimer are reduced to -1.06 eV and -0.98 eV, respectively. The negative formation energies indicate that the Ge-O2 and Ge-O3 are most likely to form during the growth. These simulation results strongly prove that there is a driving force that prompts the O binding to the Ge donor. Therefore, not only for the statistics, the Ge-O2 trimer and Ge-O3 tetramer doping are indeed favorable in the thermodynamics aspect. On the other hand, in the experiments, Ge2O3 was employed as the precursor for Ge-O doping, which actually already have the Ge-O binding before incorporation into the h-BN.

Supplementary Note 3: Energy band diagram, space charge and electric field distribution of the p-n junction
The doping level and carrier density of p-GaN should be larger than those of n-type h-BN layer. This may impact the diode behavior. The energy band diagram, space charge distribution, and electric field distribution in this p-GaN/n-hBN junction in thermal equilibrium are shown in Figure S26. For a thick n-hBN layer, the n-hBN layer is not completely depleted (a) whereas the ultrathin n-hBN should be largely depleted (b). From the electric field distribution in Figure S26, we can see that he built-in electric field Em at the depleted ultrathin h-BN interface will decrease but still work for the typical diode behavior. This decreasing built-in field with the decreasing h-BN thickness could lead to decreasing the forward turn-on voltage, which has been confirmed by the I-V test, as shown in Fig. 5(d)-(e). Therefore, the forward turn-on voltage for the monolayer h-BN case (1.44 eV) is smaller than that the 6-layer n-hBN case (3.11 eV).

Supplementary Note 4: Effective capacitance vs applied frequencies
The phenomenon of increasing capacitance with the increasing frequency is unusual for a pn junction. Generally, the capacitance should be constant over frequency. But when the applied frequencies approach the capacitor's self-resonant frequency, a parasitic series inductance will work and result in an effective capacitance (CE) that is larger than the nominal capacitance (CO). 2,3 The effective capacitance can be described as： where f is the applied frequency, LC is the parasitic series inductance of the capacitor. In practice the inductance of the capacitors is rather small so that CE = CO. When the inductance becomes considerable, at high frequencies the effective capacitance will increase along with the frequency. Thus, we can find out that the origin of the capacitance increasing in this n-hBN/p-GaN junction should be attributed to the considerable inner series inductance. By fitting the Cp-f data with above equation, as shown in Figure S27, we can obtain the value of the inner series inductance. As a result, the nominal capacitance CO is 0.2486 pF and the inductance LC is 0.0035 H. This considerable inner inductance in the n-hBN/p-GaN junction should be highly related with the unique 2D layered structure of the multilayer h-BN. Because of the weak van der Waals interaction between n-h-BN layers, the possible formation of multiple conducting micro-channels could be the reason to introduce this inner inductance. However, reliable evidences and explanations need further thorough investigations.

Supplementary method about the FET device
Instead of Hall measurement, we obtained further electrical properties of the n-type h-BN monolayer by the FET device method. 4 The resistivity ρ of n-type h-BN monolayer was calculated be about 2.29×10 4 Ω cm from the Isd -Vsd curve at Vg = 0 (Fig. 4g-i). In addition, the channel conductance of a FET device can be calculated as follow: where W and L are the width and length of the channel, is the electron mobility, is the gate capacitance. For SiO2, the gate capacitance is: where is the vacuum permittivity, is the relative dielectric constant of gate SiO2 (3.9), and d is the thickness of gate SiO2 layer. According to these two equations, the electron mobility of ntype h-BN was calculated to be 0.014 cm 2 V -1 s -1 as follow: = .
The electron mobility of n-type h-BN monolayer is relatively small, which can be contributed to the interaction and scattering effects from the SiO2 substrate. The SiO2 substrate is not smooth sufficiently and there are many dangling bonds exist on the surface. Many works have reported that the SiO2 substrate may deteriorate the mobility of 2D materials. 5,6 The relation between the resistivity, conductivity, and carrier concentration can be defined as following equation: = 1 =

.
Therefore, the electron concentration n can be calculated from： = 1 .
According to above equation, the electron concentration of n-type h-BN monolayer is determined to be 1.94×10 16 cm -3 .